An organic compound of carbon, hydrogen and nitrogen contains these elements having mass percentage 66.67%, 7.41% and 25.92% respectively. Calculate empirical formula

Options

A. C_3H_4N
B. C_2H_6N
C. C_4H_4N
D. C_4H_9N

Answer

To calculate the empirical formula of the organic compound based on the given mass percentages of carbon, hydrogen, and nitrogen, we can follow these steps:

### Step 1: Convert mass percentages to grams
Assuming we have 100 grams of the compound, the mass of each element will be equal to its percentage:
- Carbon (C): 66.67 g
- Hydrogen (H): 7.41 g
- Nitrogen (N): 25.92 g

### Step 2: Calculate the number of moles of each element
To find the number of moles, we use the formula:
\[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \]
- Moles of Carbon:
\[ \text{Moles of C} = \frac{66.67 \, \text{g}}{12 \, \text{g/mol}} = 5.56 \, \text{mol} \]
- Moles of Hydrogen:
\[ \text{Moles of H} = \frac{7.41 \, \text{g}}{1 \, \text{g/mol}} = 7.41 \, \text{mol} \]
- Moles of Nitrogen:
\[ \text{Moles of N} = \frac{25.92 \, \text{g}}{14 \, \text{g/mol}} = 1.85 \, \text{mol} \]

### Step 3: Determine the simplest mole ratio
Next, we divide the number of moles of each element by the smallest number of moles calculated:
- Smallest number of moles is for Nitrogen (1.85 mol).
- Ratio for Carbon:
\[ \text{Ratio of C} = \frac{5.56}{1.85} \approx 3 \]
- Ratio for Hydrogen:
\[ \text{Ratio of H} = \frac{7.41}{1.85} \approx 4 \]
- Ratio for Nitrogen:
\[ \text{Ratio of N} = \frac{1.85}{1.85} = 1 \]

### Step 4: Write the empirical formula
From the ratios calculated, we can express the empirical formula as:
\[ \text{Empirical Formula} = C_3H_4N_1 \quad \text{or simply} \quad C_3H_4N \]

### Conclusion
The empirical formula of the organic compound is **C3H4N**.

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